A201591 Decimal expansion of least x satisfying 6*x^2 = csc(x) and 0 < x < Pi.

5, 6, 0, 1, 0, 0, 6, 9, 4, 9, 1, 2, 1, 6, 0, 7, 6, 2, 8, 2, 3, 8, 4, 1, 3, 3, 3, 7, 9, 7, 8, 1, 2, 0, 7, 7, 5, 2, 9, 3, 7, 4, 5, 0, 3, 0, 3, 0, 8, 9, 6, 4, 1, 1, 5, 5, 8, 6, 1, 2, 2, 0, 4, 3, 0, 9, 0, 6, 7, 5, 9, 1, 6, 2, 1, 5, 6, 4, 8, 3, 3, 1, 4, 0, 8, 0, 7, 1, 6, 1, 7, 3, 2, 2, 0, 2, 3, 8, 9, 3, 3

Offset: 0

Author

Clark Kimberling, Dec 03 2011

Keywords

• nonn
• cons

Comments

See A201564 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least:  0.56010069491216076282384133379781207752937450...
greatest:  3.12451991250138769396880196501162499414487...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Index entries for transcendental numbers.

Crossrefs

Cf. A201564.

Programs

Mathematica

a = 6; c = 0;
f[x_] := a*x^2 + c; g[x_] := Csc[x]
Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201591 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
RealDigits[r]   (* A201653 *)

PARI

a=6; c=0; solve(x=0.5, 1, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 22 2018

Extensions

Terms a(90) onward corrected by G. C. Greubel, Aug 22 2018